Electron. J. Diff. Equ., Vol. 2010(2010), No. 04, pp. 1-10.

Nonlinear scalar two-point boundary-value problems on time scales

Rebecca I. B. Kalhorn, Jesus Rodriguez

Abstract:
We establish sufficient conditions for the solvability of scalar nonlinear boundary-value problems on time scales. Our attention will be focused on problems where the solution space for the corresponding linear homogeneous boundary-value problem is nontrivial. As a consequence of our results we are able to provide easily verifiable conditions for the existence of periodic behavior for dynamic equations on time scales.

Submitted March 17, 2009. Published January 6, 2010.
Math Subject Classifications: 39B99, 39A10.
Key Words: Boundary value problems; time scales; Schauder fixed point theorem

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Rebecca I. B. Kalhorn
Department of Mathematics
North Carolina State University, Box 8205
Raleigh, NC 7695-8205, USA
email: rkalhorn@gmail.com
Jesús Rodríguez
Department of Mathematics
North Carolina State University, Box 8205
Raleigh, NC 7695-8205, USA
email: rodrigu@ncsu.edu

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